Question

Length of transverse axis of a hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$ is:

Answer 1

In the figure, the points $A$ and $A^{\prime }$, where the curve meets the line joining the foci $S$ and $S^{\prime }$ are called the vertices of the hyperbola.

The coordinates of $A$ and $A^{\prime }$ are $(a,0)$ and $(-a,0)$, respectively.

The straight line joining the vertices $A$ and $A^{\prime }$ is called transverse axis of the hyperbola.

It's length $A{A}^{\prime }$ is $2a$

Thus, length of transverse axis of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$ $\Rightarrow 2a$